Robust and sparse estimators for linear regression models
- Autores
- Smucler, Ezequiel; Yohai, Victor Jaime
- Año de publicación
- 2017
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Penalized regression estimators are popular tools for the analysis of sparse and high-dimensional models. However, penalized regression estimators defined using an unbounded loss function can be very sensitive to the presence of outlying observations, especially to high leverage outliers. The robust and asymptotic properties of ℓ1-penalized MM-estimators and MM-estimators with an adaptive ℓ1 penalty are studied. For the case of a fixed number of covariates, the asymptotic distribution of the estimators is derived and it is proven that for the case of an adaptive ℓ1 penalty, the resulting estimator can have the oracle property. The advantages of the proposed estimators are demonstrated through an extensive simulation study and the analysis of real data sets. The proofs of the theoretical results are available in the Supplementary material to this article (see Appendix A).
Fil: Smucler, Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina
Fil: Yohai, Victor Jaime. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina - Materia
-
Lasso
Mm-Estimators
Oracle Property
Robust Regression
Sparse Linear Models - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/66002
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Robust and sparse estimators for linear regression modelsSmucler, EzequielYohai, Victor JaimeLassoMm-EstimatorsOracle PropertyRobust RegressionSparse Linear Modelshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Penalized regression estimators are popular tools for the analysis of sparse and high-dimensional models. However, penalized regression estimators defined using an unbounded loss function can be very sensitive to the presence of outlying observations, especially to high leverage outliers. The robust and asymptotic properties of ℓ1-penalized MM-estimators and MM-estimators with an adaptive ℓ1 penalty are studied. For the case of a fixed number of covariates, the asymptotic distribution of the estimators is derived and it is proven that for the case of an adaptive ℓ1 penalty, the resulting estimator can have the oracle property. The advantages of the proposed estimators are demonstrated through an extensive simulation study and the analysis of real data sets. The proofs of the theoretical results are available in the Supplementary material to this article (see Appendix A).Fil: Smucler, Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; ArgentinaFil: Yohai, Victor Jaime. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; ArgentinaElsevier Science2017-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/66002Smucler, Ezequiel; Yohai, Victor Jaime; Robust and sparse estimators for linear regression models; Elsevier Science; Computational Statistics and Data Analysis; 111; 7-2017; 116-1300167-9473CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.csda.2017.02.002info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0167947317300221info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:48:21Zoai:ri.conicet.gov.ar:11336/66002instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:48:21.692CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Robust and sparse estimators for linear regression models |
title |
Robust and sparse estimators for linear regression models |
spellingShingle |
Robust and sparse estimators for linear regression models Smucler, Ezequiel Lasso Mm-Estimators Oracle Property Robust Regression Sparse Linear Models |
title_short |
Robust and sparse estimators for linear regression models |
title_full |
Robust and sparse estimators for linear regression models |
title_fullStr |
Robust and sparse estimators for linear regression models |
title_full_unstemmed |
Robust and sparse estimators for linear regression models |
title_sort |
Robust and sparse estimators for linear regression models |
dc.creator.none.fl_str_mv |
Smucler, Ezequiel Yohai, Victor Jaime |
author |
Smucler, Ezequiel |
author_facet |
Smucler, Ezequiel Yohai, Victor Jaime |
author_role |
author |
author2 |
Yohai, Victor Jaime |
author2_role |
author |
dc.subject.none.fl_str_mv |
Lasso Mm-Estimators Oracle Property Robust Regression Sparse Linear Models |
topic |
Lasso Mm-Estimators Oracle Property Robust Regression Sparse Linear Models |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
Penalized regression estimators are popular tools for the analysis of sparse and high-dimensional models. However, penalized regression estimators defined using an unbounded loss function can be very sensitive to the presence of outlying observations, especially to high leverage outliers. The robust and asymptotic properties of ℓ1-penalized MM-estimators and MM-estimators with an adaptive ℓ1 penalty are studied. For the case of a fixed number of covariates, the asymptotic distribution of the estimators is derived and it is proven that for the case of an adaptive ℓ1 penalty, the resulting estimator can have the oracle property. The advantages of the proposed estimators are demonstrated through an extensive simulation study and the analysis of real data sets. The proofs of the theoretical results are available in the Supplementary material to this article (see Appendix A). Fil: Smucler, Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina Fil: Yohai, Victor Jaime. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina |
description |
Penalized regression estimators are popular tools for the analysis of sparse and high-dimensional models. However, penalized regression estimators defined using an unbounded loss function can be very sensitive to the presence of outlying observations, especially to high leverage outliers. The robust and asymptotic properties of ℓ1-penalized MM-estimators and MM-estimators with an adaptive ℓ1 penalty are studied. For the case of a fixed number of covariates, the asymptotic distribution of the estimators is derived and it is proven that for the case of an adaptive ℓ1 penalty, the resulting estimator can have the oracle property. The advantages of the proposed estimators are demonstrated through an extensive simulation study and the analysis of real data sets. The proofs of the theoretical results are available in the Supplementary material to this article (see Appendix A). |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-07 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/66002 Smucler, Ezequiel; Yohai, Victor Jaime; Robust and sparse estimators for linear regression models; Elsevier Science; Computational Statistics and Data Analysis; 111; 7-2017; 116-130 0167-9473 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/66002 |
identifier_str_mv |
Smucler, Ezequiel; Yohai, Victor Jaime; Robust and sparse estimators for linear regression models; Elsevier Science; Computational Statistics and Data Analysis; 111; 7-2017; 116-130 0167-9473 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.csda.2017.02.002 info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0167947317300221 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier Science |
publisher.none.fl_str_mv |
Elsevier Science |
dc.source.none.fl_str_mv |
reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
reponame_str |
CONICET Digital (CONICET) |
collection |
CONICET Digital (CONICET) |
instname_str |
Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.name.fl_str_mv |
CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.mail.fl_str_mv |
dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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1842268919406002176 |
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13.13397 |